Question

Audrey is trying to find the equation of a line parallel to y = 2 over 3 x −5 in slope-intercept form that passes through the point (−6, −1). Which of the following equations will she use

Answer 1

Given the line with equation
`y=(2)/(3)x-5.`

Parallel lines have the same slopes, so the parallel line has equation

`y=(2)/(3)x+a.`

This line passes through the point (-6,-1), then its coordinates satisfy the equation:

`-1=(2)/(3)\cdot (-6)+a,\\ \\a=-1+4,\\ \\a=3.`

Therefore, the equation of needed line is

`y=(2)/(3)x+3.`